We present the covering set of the squared eigenfunctions for a degenerate 3×3 eigenvalue problem. The derivation follows the approach recently outlined by Yang and Kaup on this same equation (J. Math. Phys. 50 023504 (2009)). This eigenvalue problem is important since it serves as the spectral problem for the inverse scattering transform (IST) of the vector NLS equation, the Sasa– Satsuma equa...

Abstract: In this paper, we study the application of the known generalized (G ′ G )-expansion method for seeking more exact travelling solutions solutions and soliton solutions of the Kaup-Kupershmidt equation and the (2+1) dimensional breaking soliton equation. As a result, we come to the conclusion that the traveling wave solutions for the two non-linear equations are obtained in three arbitr...

(Received 25 June 1998, revised version received 05 January 1999) The Lax pair for a derivative nonlinear Schrödinger equation proposed by Chen-Lee-Liu is generalized into matrix form. This gives new types of integrable coupled derivative nonlinear Schrödinger equations. By virtue of a gauge transformation, a new multi-component extension of a derivative nonlinear Schrödinger equation proposed ...

The equation of a motion of curves in the projective plane is deduced. Local flows are defined in terms of polynomial differential functions. A family of local flows inducing the Kaup–Kupershmidt hierarchy is constructed. The integration of the congruence curves is discussed. Local motions defined by the traveling wave cnoidal solutions of the fifth-order Kaup–Kupershmidt equation are described.

In this paper we develop a bilinearisation-reduction approach to derive solutions the classical and nonlocal nonlinear Schr\"{o}dinger (NLS) equations with nonzero backgrounds. We start from second order Ablowitz-Kaup-Newell-Segur coupled as an unreduced system. With pair of $(q_0,r_0)$ bilinearize system obtain in terms quasi double Wronskians. Then implement reductions by introducing constrai...

We construct a new multi-component CKP hierarchy based on the eigenfunction symmetry reduction. It contains two types of CKP equation with self-consistent sources which Lax representations are presented. Also it admits reductions to k−constrained CKP hierarchy and to a (1+1)-dimensional soliton hierarchy with self-consistent source, which include two types of Kaup-Kuperschmidt equation with sel...

A systematic investigation of certain higher order or deformed soliton equations with (1 + 1) dimensions, from the point complete integrability, is presented. Following procedure Ablowitz, Kaup, Newell and Segur (AKNS) we find that version Nonlinear Schrodinger equation, Hirota equation AKNS admit Lax pairs. We report each identified possesses Painleve property for partial differential admits t...

In this paper, the Lakshmanan-Porsezian-Daniel (LPD) equation is considered. This integrable and admits Lax pair. The LPD generalization of nonlinear Schrodinger (NLS) described by Ablowitz-Kaup-Newell-Segur (AKNS) system. Using sine-cosine method hyperbolic tangent a variety new exact solutions are obtained. These methods effective tools for searching partial differential equations in mathemat...

In this paper, the Exp -function method with the aid of symbolic computational system is used to obtain the exact travelling wave and solitary solutions of the Fitzhugh-Nagumo (FN), Modified Liouville equations and bi-directional Kaup-Kupershmidt (bKK) equation (sixth-order nonlinear equation). An attempt has been made to show the capabilities and wide-range applications of the Exp -function me...